1. Field of the Invention
The invention relates to a signal processor with local signal behavior and predictive capability. In particular, the invention provides a method and apparatus for sampling an input signal, determining characteristics of the signal and predicting future characteristics of the signal.
2. Description of the Related Art
Many conventional signal processing techniques are known in the art. Many of these techniques include time domain and frequency domain computation and analysis. Popular examples of such computation and analysis includes Fourier expansion and Fourier transforms as described in U.S. Pat. No. 6,115,726.
While there are known techniques for computing and analyzing a signal, these conventional techniques are insufficient to manage high data rates that are naturally part of the communication revolution occurring in advanced technology. For example, communication standards are now being implemented in the range of 40 gigabits per second, which several years ago would have seemed nearly impossible to achieve. In this context, there are specific features that are important and those are described as follows.
Given a signal up to a time L, it would be advantageous to know some information about the future behavior of the signal. This general problem has several different interpretations: first, it could be a question regarding an estimate of the signal""s value at some future time t greater than L; second, it could be a question regarding an estimate of several derivatives f(i)(L) of f(t) at the time limit L; or third, one can even combine these cases, asking for an estimate of derivatives of f(t) at a future time f(i)(t). Ideally, answers to these questions should extract parameters of the signal which allow one to easily vary the time, t, and order of differentiation, i.
In one embodiment of the present invention, a method of predicting the behavior of an input signal is disclosed. The input signal is a band-limited analog signal. The method includes representing the input signal as a truncated series at a first time. The first time is at or before a time limit. The truncated series includes local signal behavior parameters (LSBPs). The method also includes predicting the behavior of the input signal using the LSBPs.
In an aspect of this embodiment, the method also includes calculating the LSBPs by fitting the truncated series to discrete signal samples at a second time. This second time is before the time limit.
In another embodiment of the present invention, a method of predicting the behavior of an input signal is disclosed. The method includes representing the signal as a first truncated series at a first time. The input signal is a band-limited analog input signal. The first time is at or before a time limit. The first truncated series includes a first number of local signal behavior parameters (LSBPs). The method also includes calculating the first number of LSBPs by fitting the first truncated series to discrete signal samples and representing the input signal as a second truncated series at a second time. The second time is after the first time, and the second truncated series includes a second number of LSBPs. The method further includes calculating the second number of LSBPs by simultaneously fitting the second truncated series to discrete samples of the input signal at points in time less than the time limit, and values of the input signal and derivatives of the input signal about the first time, wherein the values are determined by the first number of LSBPs. The method still further includes predicting the behavior of the input signal using the second number of LSBPs.
In another embodiment of the present invention, a signal processor is disclosed. The signal processor includes a differentiator and an extrapolator coupled to the differentiator. The differentiator is configured to receive an input signal and to generate a vector. The input signal is band-limited. The vector includes at least one chromatic derivative. The extrapolator is coupled to the differentiator and is configured to generate an output signal.
The foregoing is a summary and thus contains, by necessity, simplifications, generalizations and omissions of detail; consequently, those skilled in the art will appreciate that the summary is illustrative only and is not intended to be in any way limiting. As will also be apparent to one of skill in the art, the operations disclosed herein may be implemented in a number of ways, and such changes and modifications may be made without departing from this invention and its broader aspects. Other aspects, inventive features, and advantages of the present invention, as defined solely by the claims, will become apparent in the non-limiting detailed description set forth below.